How to do curves in a mesh
this should be easily accomplished with a screw modifier.

all you need to do is create the profile of the dog bowl.



Once you do, it will be imperative to put the vertex that marks the center of the bowl on the origin of the object. you can do this by selecting this vertex and Shift+S>Cursor to selected Shift+Ctrl+Alt+C>origin to 3D cursor

Now add the screw modifier. you can set the amount of turn it goes for higher detail.